While I've never owned (or wanted to) a popup, I am in the process of stripping one down for a utility trailer. In doing so. I noticed a few things...
1. Water damage around the wheel cavities. Apparently there was a leak where the wheel well sealed onto the floor, and the floor started rotting out. Not a large area, but it's there and difficult to inspect since the area of the floor affected was under the fridge and could not be accessed.
2. Water damage in the wall behind the fridge. Not sure how or why. I am assuming the canvas leaked at some point and was replaced. Not rotted bad, but the damage was there.
3. Water damage under the rear dinette seat, center of the trailer. There was a storage area that stretched from one side to the other and the floor is weak in the middle. I'm suspecting there is a leak where the spare tire mounts on the back and water runs into the wall and into the floor.
4. Inspect the rooftop for "flatness". If it sags a bit in the middle while raising the roof (raised about a foot from closed position) there could be stress or water damage. Either way, you do not want a puddle in the middle of the roof when it rains. If the roof seems heavy, it could be waterlogged. The roof is Styrofoam glued on both sides and sandwiched between sheets of aluminum. It should be lightweight and solid. Wet Styrofoam is very heavy.
5. Carefully examine the lift mechanism for wear. Cables should be shiny and there should be NO STRAY STRANDS. Pivot points should be snug, not loose. A support arm that wobbles when half open would be a concern.
6. Canvas wear is OK depending on how bad, and might be a tool to negotiate a price reduction. You don't want patches, cracks, or holes. The plastic windows should be inspected too. Zip and unzip every zipper.
7. As noted by go6car, MOLD IS BAD. Any mold found means the conditions are or were right for mold growth during storage and there WILL BE mold where you cannot easily inspect.
8. Tires should not be "old". They should have a datecode and you do not want to run tires more than 7 years old. Regardless of the tread they may have, old tires are weakened internally and can blow out at any time. A blowout can cause serious damage to the underside of the floor.
I would take a small rubber hammer and "thump" the floor around the edges. A soft spot sounds quite different than a solid one and a reasonably cheap new linoleum floor covering can hide a lot. Test every part of the floor you can including underneath. While you are under it, look for signs of scraping or abuse that might compromise the frame or structure.
Inspect the edges and corners inside. If it looks like they didn't keep it clean, then they probably didn't maintain it too well. Look in the fridge too. Look particularly around the seal for signs of embedded crud in the corner where your hand opens the fridge. Don't be afraid to pull the seal out just a bit to look deep into the gap between the seal and the door. Take a strong flashlight and inspect everything you can see including storage areas. Shine the flashlight across the wall to look for a rippled surface. Rippled plywood is an indicator of water damage.
Sounds like a lot of work, but that's why they get the big bucks to inspect it for you.
Joe